A Very Relaxed Control Law for Bearing-Only Triangular Formation Control

Abstract

The problem of bearing-only triangular formation control is considered. Each agent measures two inter-agent bearings in a local coordinate system and is tasked with establishing, and maintaining, a desired angular separation relative to its neighbours (and consequently an overall desired shape). A distributed control law is designed for each agent that is based only on the agent's locally measured bearings. A strong convergence result is established which guarantees global exponential convergence of the formation to the desired shape. Despite the convergence guarantee, the controller is also relaxed in the sense that each agent can independently choose their control inputs within a large region of values. The proposed controller is robust to a single agent motion failure or a common group motion command.